In the United States, Broadway has long been the center of the nation's theatre, but beginning in the 1950s, that began to change.
Fire codes and labor regulations prevented certain forms of artistic experimentation, such as performing shows in the round, so small companies like Circle in the Square began operating under cabaret licenses in order to skirt the rules. These plays were usually performed outside of the "Broadway Box" between 40th Street and 54th Street, so they came to be known as Off-Broadway.
Eventually the term Off-Broadway was defined as theatres with 100 to 499 seats. These theatres' smaller seating capacity allows them to have different performance contracts than Broadway houses. The emergence of Off-Broadway theatres allowed for an increased variety on New York stages, including the performance of classic plays and works of European modernism that would otherwise not have reached American audiences.
However, most American playwrights were still unable to get their plays produced either on Broadway or in Off-Broadway houses, so many began turning to even smaller stages, with fewer than 100 seats and operating with non-union performers or under union waivers. In the 1960s and 1970s, a number of enterprising individuals ran small spaces where theatre artists could produce their own work. These included Joe Chino who opened up his Café Chino to nearly anyone who asked, Ellen Stewart who founded LaMama Experimental Theatre Club as an allegedly private club in order to get around fire codes, and Ralph Cook whose Theatre Genesis operated out of St. Mark's Church in-the-Bowery.
The venues they created became known as Off-Off-Broadway, and they offered a home to playwrights unable to get produced elsewhere. Some began their careers Off-Off-Broadway with experimental plays and went on to Off-Broadway and even Broadway stages. Sam Shepard, for instance, began writing obscure pieces for Off-Off-Broadway, but was later canonized when his 1978 play Buried Child won the Pulitzer prize for drama.
One of the landmark Off-Off-Broadway productions of the 1960s was Promenade, a surreal musical comedy written by Cuban-American playwright María Irene Fornés with music by Al Carmines. After having a short run Off-Off-Broadway at Judson Memorial Church, it went on to have a commercial Off-Broadway run in 1969.
Fornés achieved great acclaim as an experimental playwright with Fefu and Her Friends, a play that after an opening scene, divides the audience into four groups and has them watch the same four scenes, but in different orders. At the end of the play, the audience convenes again in the same spot to watch the play's conclusion together, though they have experienced the story in four distinctly different ways.
Fefu and Her Friends recently had an Off-Broadway production at Theatre for a New Audience in Brooklyn. Sadly, I missed it. (And now I'm missing theatre a lot...)